Advertisements
Advertisements
प्रश्न
Use ruler and compass only for answering this question.
Draw a circle of radius 4 cm. Mark the centre as O. Mark a point P outside the circle at a distance of 7 cm from the centre. Construct two tangents to the circle from the external point P.
Measure and write down the length of any one tangent.
Advertisements
उत्तर
Steps of Construction:
- Draw a circle with centre O and radius 4 cm using a compass.
- Mark a point P on a horizontal line such that OP = 7 cm.
- Join OP.
- Draw the perpendicular bisector of OP to obtain its midpoint, say M.
- With M as centre and radius MO, draw a circle.
- This circle will cut the given circle at two distinct points A and B.
- Join PA and PB.
- PA and PB are the required tangents from the external point P to the given circle.
Measure the length of the tangent.
Length of tangent
`sqrt(OP^2 − "radius"^2)`
= `sqrt(7^2 − 4^2)`
= `sqrt(49 − 16)`
= `sqrt(33)`
= 5.74 cm (approximately)
So, the length of one tangent is 5.74 cm.
APPEARS IN
संबंधित प्रश्न
Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle.
Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q. Give the justification of the construction.
In the given figure, PQ is a tangent to the circle at A. AB and AD are bisectors of ∠CAQ and ∠PAC. if ∠BAQ = 30°. Prove that:
- BD is a diameter of the circle.
- ABC is an isosceles triangle.
Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6.2 cm from its centre.
Draw a circle of radius 3.5 cm. Take two points A and B on one of its extended diameter, each at a distance of 5 cm from its center. Draw tangents to the circle from each of these points A and B.
Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
Use a ruler and a pair of compasses to construct ΔABC in which BC = 4.2 cm, ∠ ABC = 60°, and AB 5 cm. Construct a circle of radius 2 cm to touch both the arms of ∠ ABC of Δ ABC.
Draw two lines AB, AC so that ∠ BAC = 40°:
(i) Construct the locus of the center of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose center lies within the ∠ BAC.
Which of the following is not true for a point P on the circle?
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
